Tensor renormalization group with randomized singular value decomposition

Satoshi Morita, Ryo Igarashi, Hui-Hai Zhao, and Naoki Kawashima
Phys. Rev. E 97, 033310 – Published 20 March 2018

Abstract

An algorithm of the tensor renormalization group is proposed based on a randomized algorithm for singular value decomposition. Our algorithm is applicable to a broad range of two-dimensional classical models. In the case of a square lattice, its computational complexity and memory usage are proportional to the fifth and the third power of the bond dimension, respectively, whereas those of the conventional implementation are of the sixth and the fourth power. The oversampling parameter larger than the bond dimension is sufficient to reproduce the same result as full singular value decomposition even at the critical point of the two-dimensional Ising model.

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  • Received 1 December 2017

DOI:https://doi.org/10.1103/PhysRevE.97.033310

©2018 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Satoshi Morita1,*, Ryo Igarashi2, Hui-Hai Zhao3, and Naoki Kawashima1

  • 1The Institute for Solid State Physics, The University of Tokyo, Kashiwa, Chiba 277-8581, Japan
  • 2Information Technology Center, The University of Tokyo, Bunkyo-ku, Tokyo 113-8658, Japan
  • 3RIKEN Brain Science Institute, Wako-shi, Saitama 351-0198, Japan

  • *morita@issp.u-tokyo.ac.jp

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Issue

Vol. 97, Iss. 3 — March 2018

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